It is common practice to use adaptive noise cancellation devices in the transmission of intelligible speech from an environment with considerable acoustic noise, such as an aircraft cockpit, a car etc., utilizing as a reference signal the signal from an additional microphone, located sufficiently far from the speaker to be insensitive to the speech of the speaker and as close as possible to the noise source. Adaptive noise cancellation devices are also used in full-duplex speakerphone applications to prevent howling resulting from the feedback path between speaker and microphone of the speakerphone device.
Various techniques for adaptive noise cancelling are known, some of these are described in a paper by B. Widrow et al, "Adaptive Noise Cancelling--Principles and Application of the LMS adaptive filter", Proc IEEE, Vol 63, No 12, Dec 1975, pp 1692-1716, and in a paper by M. R. Sambur, "Adaptive Noise Cancelling for Speech Signals", IEEE trans. ASSP, vol 26, 1977, pp 419-423.
An adaptive noise canceller first produces an estimate of the characteristics of the transformation from the reference noise signal to the noise component of the signal at the main microphone. This transformation actually depends on two acoustic coupling paths: the first between the noise source to the additional microphone, the second between the noise source to the main microphone. Then the reference noise signal is used to model the noisy signal component at the main microphone. This noise component is subtracted from the actual microphone signal. In the absence of the speaker signal and assuming that the transformation is exactly identified, the difference between the actual main microphone input and the estimated noise at the adaptive filter output would be zero. In the presence of the speaker signal this difference signal contains mainly the signal from the speaker.
The filter characteristics are dynamically changed for optimum removal of the noise signal. The two acoustic paths, which define the transformation between the additional and the main microphone are generally nonstationary. The adaptation rate has to be sufficiently high to adaptively track changes in the impulse responses of these paths due to the movement of people or objects in the room, the movement of the noise source or the change in the noise characteristics.
Adaptive filters usually employ the well established "LMS algorithm", which is known also by the name "stochastic gradients", see, for example, Widrow B, et al "Stationary and Nonstationary Learning Characteristics of the LMS Adaptive Filter", Proc IEEE, August 1976, Vol 64, No 8, PP 1151-1162.
According to the LMS algorithm, the output of the adaptive filter is required to be as small as possible in the sense of least-mean-square error, ie the output power is minimized. The LMS algorithm updates N unknown filter coefficients each input sample and produces an approximately optimal solution in O(N) computations. The LMS algorithm works best when the reference signal is a white noise signal. However, for actual signals which differ from a white noise, and are non-stationary, the convergence of the LMS method is very poor.
The required filter length, ie the number of taps N, is determined by the length of impulse responses of the acoustic leakage paths, that is by the reverberation times of the room. Typical reverberation time of most rooms is less than 400 msec. The adaptive filter length must therefore be about 100 to 200 msec, ie in the range of 1000 to 2000 taps for a common choice of sampling frequency of 8 KHz. Not counting the filtering operation itself, the computational requirements for adaptive LMS filter implementation are therefore at least in the range of 16 to 32 million instructions per second--a very substantial amount of computing power.
Another approach to the problem of adaptive noise cancellation is known as the sub-band acoustic echo canceller (SBAEC), see for example a paper by Andre Gilloire, "Experiments with Sub-Band Acoustic Echo Cancellers for Teleconferencing", Proc of IEEE ICASSP 87, April 1987, pp 2141-2144. These have advantages over the standard LMS method both in adaptation rate and in computational complexity. They do, however, have a residual error due to channel interdependence, which has not been taken into account in the adaptation scheme, and this limits the number of channels and therefore the computational improvement which may be obtained.